I would say the quest's get discarded after ecpic quest expires. (even if it nowhere says it should)It makes sense because otherwise you would have 6 quest avaible instead of the normal 5.

Imagine the event "new horizons" (where you can discard 1 quest to draw another), after epic quest expires and you have 6 quests active - you can discard the epic 1, draw another and have 6 avaible, and since now it nowhere states that you do not draw another quest after completing an active, you have 6 quest avaible for the rest of the game.